Begin by opening the can of mackerel and draining the brine. Place the mackerel into a mixing bowl and use a fork to flake the fish into smaller pieces.
Add the eggs, grated Parmesan cheese, breadcrumbs, mayonnaise, mustard, and chopped chives or scallions to the bowl with the flaked mackerel. Use the fork to thoroughly mix everything together until well combined.
Using your hands, take a portion of the mixture and form it into a patty, about 2-3 inches in diameter. Repeat this process until all the mixture is used up.
In a frying pan, heat a generous amount of avocado oil over medium heat.
Once the oil is hot, carefully place the patties in the pan, making sure not to overcrowd them. Cook for about 3-4 minutes on each side, or until they are golden brown and crispy.
Once cooked, transfer the patties to a plate lined with paper towels to drain any excess oil. Serve warm with your favorite dipping sauce or alongside a fresh salad.